The kinetics of singlet fission (SF) (i.e., spontaneous splitting of the excited singlet state into a pair of triplet (T) excitons (TT-pair)) is known to be significantly affected by TT-annihilation (TTA), which manifests itself in magnetic field effects on the TTA and, in particular, in the magnetic-field dependence of the SF-kinetics. In this study, in the two-state model (TSM), a method is proposed for treating the magnetic field effects on the SF-kinetics, which allows for the correct description of the manifestation of the stochastic migration of T-excitons assuming that the manifestation results from the transition from two states of coupled and freely diffusing T-excitons. In the TSM, the analytical expression for the magnetic-field-dependent part of the SF-kinetics is derived. This expression is applied to the analysis of the SF-kinetics measured in amorphous rubrene films in the absence of a magnetic field and in the field B = 8 kGs.

In recent years numerous satellite data on the yellow glow of the sodium layer (located at an altitude of 85–95 km from the Earth’s surface) have become available. Studies of optical activity at sodium D‑line frequencies are necessary for a better understanding of the plasma-chemical processes occurring in the mesosphere. It should be taken into account that these processes occur in a neutral environment, where molecular nitrogen is the main component. In this study the analytical numerical expressions for the elements of a 3 × 3 matrix of the interaction between Na(2Pj) and N2( X^1Σ _g^ + ) and the interaction potential between Na(2S1/2) and N2( X^1Σ _g^ + ) are obtained at medium and large interparticle distances that determine the collisional broadening of the radiation lines. The exchange, quadrupole–quadrupole, dispersion, and spin–orbit interactions are taken into account. The exchange interaction between the valence Na electron and N2( X^1Σ _g^ + ) molecule is described by the local Hellman pseudopotential. The effect of the overlap between Na(2S1/2,2Pj) and N2( X^1Σ _g^ + ) electron densities is taken into account in the evaluation of long-range quadrupole–quadrupole and dispersion interactions.

The kinetics of the decay (splitting) of the excited singlet S_1^* -state of rubrene molecules into a pair of triplet-excitons (T-excitons) in rubrene films, usually represented in terms of the kinetics ps(t) of the decay of fluorescence (KDF) from the S_1^* -state, is analyzed in detail. The KDF is known to be significantly controlled by the process of diffusive migration and annihilation of the generated T-excitons. In the analysis, two migration models are considered: the two-state model (TSM), treating the migration effect as a result of transitions between the [TT] state of coupled T-excitons (at small TT-distances r) and the [T+T]-state of freely migrating T-excitons (at large distances r), as well as the free migration model (FMM), neglecting the effect of the [TT] state. Within the TSM and FMM, the expressions for ps(t) are derived, which are applied to describe the KDF p_s^exp( t ) , measured in amorphous rubrene films. Within the experimentally investigated range of times, 0.4–200 ns, the TSM is shown to reproduce the behavior of the experimental KDF p_s^exp( t ) much more accurately than the FMM. At longer times t ≳ 1pt 103 ns, a substantial difference ( ≳ 1pt 25% ) between p_s^exp( t ) and the FMM-predicted KDF ps(t) is found, which is far beyond the experimental error ( ≲ 3

В настоящей работе впервые прямым способом в мезоскопическом масштабе длин решена «флуктуационная теорема». Получено аналитическое выражение для парной корреляционной функции критического состояния флюида, параметром которой является дисперсия плотности, легко восстанавливаемая из оптических экспериментов. Сравнение нашего результата с парной корреляционной функцией Орнштейна—Цернике позволило определить поправку Фишера η = 0,25, повышающую сходимость. Показано, что полученные результаты дают надежную теоретическую основу для оптической диагностики статистического состояния критических флюидов. In this paper we have solved the «fluctuation theorem» on the mesoscopic length scale for the first time in a direct way. An analytical expression for the pair correlation function of the critical state of fluid was obtained, where the density variance is the parameter that could be easily defined by optical measurements. By comparison of our result with the Ornstein—Zernike pair correlation function we have got the Fisher index η= 0.25 to increase the convergence. It was shown that the obtained results provide a reliable theoretical basis for optical diagnostics of the critical state of fluids.

В настоящее время большое внимание исследователей уделяется многоуровневому моделированию сложных газофазных физико-химических процессов, протекающих в атмосфере, при горении и в плазмохимических установках. Одним из важнейших микроскопических процессов, определяющих перенос излучения в указанных системах, является уширение спектральных линий при столкновениях излучающих атомов с атомами в основном состоянии. В данной работе предложена формулировка единой франк-кондоновской теории уширения спектральных линий в газах в терминах теории медленных атомных столкновений и неадиабатических переходов. Это позволяет по виду адиабатических потенциальных кривых сталкивающихся атомов выбирать наиболее эффективные каналы приводящих к уширению столкновений и на этой основе применять достаточно простые модели, разработанные в теории неадиабатических переходов. В качестве примера использования такого подхода проведены расчеты центра и крыльев контура спектральной линии излучения Ar( 3 P 1 ) → Ar( 1 S 0 ) возбужденных атомов аргона в собственном газе.

The manifestation of short-time (geminate) and long-time (bimolecular) stages of diffusion-controlled triplet--triplet annihilation (TTA) in the kinetics of singlet fission (SF) (i.e. splitting of the excited singlet state S*1 into a pair of T-excitons) in molecular organic semiconductors are analyzed in detail. In this analysis, the short-and long-time parts of the SF-kinetics (kinetics of fluorescence I(t) from S*1-state), are assumed to be governed by geminate and bimolecular TTA, respectively. Within the analysis, the analytical formula is derived, which is shown to fairly accurately describe the experimental SF-kinetics in the wide range of times.

В работе детально проанализированы особенности кинетики распада (расщепления) возбужденного синглетного состояния (РСС) на пару триплетных (Т) экситонов (ТТ-пару) в анизотропных молекулярных кристаллах. Эти особенности, как известно, существенно определяются обратной ТТ-аннигиляцией (т.е. аннигиляцией пар Т-экситонов, мигрирующих в объеме кристалла). В предлагаемом анализе кинетика (контролируемых аннигиляцией) процессов РСС описывалась в рамках модели двух состояний (МДС), в которой взаимодействие мигрирующих Т-экситонов ассоциируется с переходами между двумя кинетическими состояниями ТТ-пар: [ТТ]-состояния связанных пар и [Т+Т]-состояния свободно мигрирующих экситонов. Эта модель позволяет представить эффекты миграции и взаимодействия экситонов в РСС-кинетике в терминах решеточных функций Грина, выражения для которых могут быть найдены в аналитическом виде. В данной работе МДС применена для анализа кинетики РСС в кристаллах рубрена, ранее измеренной в широком диапазоне времен. Анализ дал возможность получить важную информацию о кинетических особенностях процессов РСС в анизотропных кристаллах. Показано, например, что формирование [TT]-состояния приводит к заметному искажению формы кинетической зависимости РСС на малых временах порядка времени первичной стадии этого процесса. Показано также, что анизотропия миграции Т-экситонов существенно проявляется в характерных особенностях поведения кинетики РСС на больших временах.

A great deal of attention is being paid by researchers to the multilevel modeling of complex gas-phase physicochemical processes occurring in the atmosphere, during combustion, and in plasma-chemical installations. One of the most important microscopic processes determining the transfer of radiation in these systems is the broadening of spectral lines in collisions of radiating atoms with atoms in the ground state. In this paper, we propose a formulation of the unified Franck-Condon theory of the broadening of spectral lines in gases in terms of the theory of slow atomic collisions and nonadiabatic transitions. This makes it possible to select the most efficient channels leading to the broadening of collisions based on the form of the adiabatic potential curves of the colliding atoms and, on this basis, apply fairly simple models developed in the theory of nonadiabatic transitions. As an example of using this approach, the center and wings of the of the spectral line contour of the Ar( 3 P 1 ) → Ar( 1 S 0 ) emission of excited argon atoms in their own gas are calculated.

In this study, the specific features of the kinetics of singlet fission (SF)—i.e., spontaneous splitting of the excited singlet state into a pair of triplet (T) excitons (TT-pair)—in anisotropic molecular crystals are analyzed in detail. These features are known to be primarily determined by the TT-annihilation of the created TT-pairs (migrating in the crystals). In our analysis, the kinetics of annihilation-affected SF processes is described in the two-state model (TSM), in which the interaction of migrating T-excitons is associated with transitions between two kinetic states of TT-pairs: [TT]-state of coupled TT-pairs and [T+T]-state of freely migrating T-excitons. The TSM makes it possible to represent the effects of migration and interaction on SF-kinetics in terms of the lattice Green’s functions, for which the analytical formulas are obtained in this study. The TSM is applied to the analysis of SF-kinetics in the rubrene single crystals recently measured in a wide time range. The analysis provides detailed information on some characteristic kinetic properties of SF processes in anisotropic crystals. It is shown, for example, that the formation of the [TT]-state in the SF process results in some distortion of the shape of the SF kinetic dependence at short times (of the order of the primary-stage time of SF kinetics). Is also demonstrated that the anisotropy of T-exciton migration manifests itself in some characteristic features of SF kinetics at long times.

A fundamental problem of the optical diagnostics of the supercritical fluid (SF) structure and its statistical properties in the vicinity of the Widom line is considered. The solution of this problem requires approaches that allow us to bring the peculiarities of optical measurement data in line with the peculiarities of the state of the fluid. The results obtained in the past ten years on the problem of the Widom lines in nonpolar supercritical media are briefly reviewed. Particular attention is given to the optical measurement data in the Widom region, namely, measurements of the nonlinear contribution to the refractive index and measurements of the Rayleigh light scattering intensity. It is demonstrated that these data can serve as a base for mutually complementary methods for the optical diagnostics of an SF state. As an example, the data on small-angle light scattering by SF-CO2 were used to restore its pair correlation function, the temperature dependence of which fundamentally differs from that of the Ornstein–Zernike pair correlation function. It is noted that the method based on measuring the Rayleigh scattering intensity is general in nature and can be applied to any random unordered molecular media, including the atmosphere.

Kinetics of singlet fission (SF) in molecular semiconductors, i.e., spontaneous splitting of the excited singlet state into a pair of triplet (T) excitons, is known to be strongly affected by geminate annihilation of created TT-pairs. In our work, we analyze in detail the specific properties of SF-kinetics in highly anisotropic molecular crystals (in which T-excitons undergo strongly anisotropic hopping migration) within the earlier proposed two-state model (TSM). This model allows for accurate treatment of the characteristic effects of anisotropic relative migration of T-excitons and TT-interaction on SF-kinetics, describing these effects within the approximation, that assumes kinetic coupling of two states: the [TT]-state of interacting TT-pairs and the [T + T]-state of freely migrating T-excitons. The TSM makes it possible to represent the TT-migration and interaction effects in terms of lattice-migration Green's functions, accurate analytical formulas that are obtained in this work. The TSM is applied to the analysis of SF-kinetics in rubrene single crystals, recently measured in a wide range of times (0.1 ns < t < 104 ns). The analysis enables one to obtain important information on specific properties of SF-kinetics in highly anisotropic crystals. In particular, the observed specific "hump" of SF-kinetics at intermediate times can be treated as a manifestation of the TT-coupling in the [TT]-state. It is also found that the characteristic asymptotic time-dependence of SF-kinetics (∼t-3/2) can markedly be distorted by spin relaxation in TT-pairs.

A model is constructed for the Mn^2 + (6A) excitation in manganese-doped ZnCdS quantum dots (QDs) by a femtosecond laser pulse with the carrier frequency close to the frequency of the radiation transition between the edge of the valence band and the edge of the conduction band. The model is based on the fact that the excited 4T state of the Mn2+ ion localized close to the trapped electron with energy in the forbidden zone is mixed by the exchange interaction with the states of electrons in the conduction zone of the QD. The model describes the experimentally observed, at very short delay times between the pump and probe laser pulses, radiation stimulated by the probe pulse growing with an increasing delay time at a frequency corresponding to the transition 4T → 6A in Mn^2 + .

The manifestation of specific features of T-exciton migration in the shape of low field resonances (LFRs) in the magnetic field effects on the TT-annihilation in molecular crystals is studied in detail. The LFRs are shown to be caused by avoided crossing of spin-levels of T-excitons in magnetic fields nearly parallel to the axis of the zero field splitting interaction tensor. Simple and accurate formulas for the shape of the LFR-line are derived within the hopping model of T-exciton migration. With these formulas, we demonstrate that the LFR-line shape is fairly sensitive to the anisotropy of T-exciton migration, in particular, in quasi-one-dimensional (quasi-1D) and quasi-two-dimensional (quasi-2D) limits of exciton migration. The analysis of the shape is shown to allow for obtaining the magnitude of the small rate of jumps out of 1D and 2D spaces of fast migration in the cases quasi-1D and quasi-2D migration, respectively. In addition, this analysis enables one to obtain the spin relaxation rate of T-excitons.

Kinetics of singlet fission (SF) in organic semiconductors, associated with spontaneous splitting of the excited singlet state (S1) into a pair of triplet (T) excitons, is known to be strongly affected by geminate annihilation of generated TT-pairs. In this work, we analyze in detail the SF-kinetics within lattice-migration (hopping), diffusion-migration, and exponential-kinetics two-state models (TSMs), which allow us to accurately describe the effects of relative T-exciton migration in TT-pairs. In the proposed TSMs, the migration effects are treated within the approximation of kinetic coupling of two states: [TT]-state of interacting TT-pairs and [T + T]-state of freely migrating T-excitons. The TSMs are applied to study some important specific properties of the kinetics of SF-processes in the external magnetic field. In our work, we concentrate on the analysis of T-exciton-migration effects on SF-kinetics. It is demonstrated, in particular, that the anisotropy of T-exciton migration strongly manifests itself in SF-kinetics, especially in its (inverse-power type) long time part. High migration anisotropy also leads to a substantial decrease in the rate of T-exciton escape from [TT]-state and thus to TT-caging which can result in crossing of SF-kinetic curves corresponding to different magnetic fields. The analysis of this effect is shown to provide important information on specific features of the kinetics of SF-processes.

The pulsed version of the reaction yield detected magnetic resonance (RYDMR) method is theoretically considered for the reaction scheme according to which the annihilation of triplet excitons in a molecular crystal occurs. Analytical expressions are obtained that describe the kinetics of prompt fluorescence decay with time under the conditions of its excitation by an ultrashort laser pulse. The corresponding shape of the decay curves of prompt fluorescence is determined. It is shown that the obtained curves can be used for a more detailed determination of the reaction rate constants than in the case of the stationary version of the RYDMR method.

Experimental investigations of magnetic field dependent kinetics of singlet fission (SF)processes in some organic semiconductors [i.e. splitting of excited singlet (S_1) state into a triplet exciton pair] have revealed the important specific feature of obtained kinetic curves, associated with decaying intensities I(t) of fluorescence from S_1-state. Kinetic curves, measured in different magnetic fields, are found to cross each other. We show that this kinetic curves crossing (KCC) effect is a general feature of geminate condensed phase reactions, resulting from simple characteristic properties of kinetic schemes of processes. Specific features of the KCC-effect are analyzed in detail with some models of SF-processes.

The kinetics of fast fluorescence decay in organic semiconductors due to the splitting of the excited singlet state S1 into a pair of triplet (T) excitons is significantly influenced by the process of reverse TT annihilation. It is shown that a correct interpretation of this effect requires taking into account the stochastic migration of T excitons. A two-state model (TSM) is proposed for describing the effect of migration on the kinetics of TT annihilation and, thus, on the kinetics of the fission of the S1 state. In the TSM, the migration effect is interpreted in terms of transitions between the [TT] state of the interacting excitons (at small T−T distances) and the [T + T] state of freely diffusing excitons (at large T−T distances). Within the framework of the TSM, an analytical expression for the fluorescence decay kinetics (FDK) \(I_{S_1 } (t)\) from the S1 state is derived. This expression is used to describe the FDK measured in amorphous rubrene films in the absence of the magnetic field (B = 0) and in the magnetic field B = 8.1 kG. Adjusting the parameters of the model makes it possible to reproduce the experimentally measured FDK with good accuracy. An analysis of the theoretical FDK obtained revealed a significant contribution of T migration to \(I_{S_1 } (t)\), which manifests itself, in particular, in the characteristic dependence \(I_{S_1 } (t) \sim t^{ - 3/2}\) at long times.

The contribution to the RYDMR spectrum from an elementary event of collision of two triplet excitons during their mutual annihilation is calculated, and the reverse process of photogeneration of a pair of triplet excitons in a molecular crystal are considered. The interaction between the excitons in the cell is assumed weak in comparison with the Zeeman splitting and the fine-structure parameters for the triplet state of each of the molecules. For both the annihilation of excitons and the photogeneration of a pair, the RYDMR signal from a single-crystal sample disappears at certain orientations of the crystal relative to the external magnetic field. This effect was previously experimentally observed for the anthracene−tetracyanobenzene crystal and was explained in the case of stationary optical excitation of the molecule. The results obtained in this paper make it possible to consider an arbitrary, not only stationary, mode of irradiation sample. An interval of angles between the static magnetic field and the crystallographic axes of the crystal within which the lines in the spectrum can disappear is determined. The possibility of using the RYDMR method for studying nanosized objects, for which additional peaks in the RYDMR spectrum may arise, is briefly discussed.